For any integer n>2, the n-fold cyclic branched cover M of an alternating prime knot K in 3-sphere determines K, meaning that if ′ is a not equivalent to then its cannot be homeomorphic M.

We extend the construction of Y-type invariants to null-homologous knots in rational homology three-spheres. By considering m -fold cyclic branched covers with a prime power, this extension provides new knot concordance S 3 . give computations some these for alternating and reprove independence results smooth group.

Prime power fold cyclic branched covers along smoothly slice knots all bound rational homology balls. This phenomenon, however, does not characterize knots. In this paper, we give a new construction of non-slice that have the above property. The sliceness obstruction comes from computing twisted Alexander polynomials, and introduce techniques to simplify their calculation.